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\setlength\subproofhorizspace{1em}
\begin{logicproof}{0}
\forall x \; (P(x) \imp Q(y)) & prem.\\
\forall y \; (P(y) \land R(x)) & prem.\\
P(t) \imp Q(y) & $\forall \mathrm{e}$ 1\\
P(t) \land R(x) & $\forall \mathrm{e}$ 2\\
P(t) & $\land \mathrm{e}_1$ 4\\
Q(y) & $\imp \mathrm{e}$ 3\\
\exists x \; Q(x) & $\exists \mathrm{i}$ 6
\end{logicproof}